A British man condemned to die in China on Tuesday morning may not be told the time of his execution until 24 hours beforehand, campaigners claimed today.

Two cousins of Akmal Shaikh were due to arrive in Urumqi, north-west China, today to make a final plea to the authorities for clemency towards the former minicab operator from north London.

Gordon Brown and the foreign secretary, David Miliband, are among those who have made more than 10 formal British appeals to China not to execute Shaikh, who campaigners say has severe mental illness. Failure to prevent the execution may have a significant impact on relations with China.

It was not clear whether Shaikh faced death by bullet to the head or by lethal injection. The Chinese have said knowledge of his execution is being withheld from the prisoner on "humanitarian grounds", according to the human rights campaign group Reprieve.

Clive Stafford-Smith, director of Reprieve, said: "The timing of Akmal's notice of his own execution raises obvious concerns. We hope that the Chinese authorities have kept him in the dark that his execution is only hours away because they are intending to show clemency. Only then would it be truly humanitarian for him to be the only person in the world not allowed to know.

"I have been in constant contact with Akmal's family, and they are simply praying for a reprieve, fearing for the health of his mother, who is very frail."

Efforts to save the life of Shaikh, 53, have mounted over the last few days after last week's decision by the Chinese supreme court to reject his appeal.

His brother Akbar and daughter Leilla have both begged for him to be spared, and his first cousins Soohail and Nasir Shaikh hope to see him tomorrow and deliver a petition to the court in Urumqi.

The petition says: "We plead for his life, asking that a full mental health evaluation be conducted to assess the impact of his mental illness, and that recognition be made that he is not as culpable as those who might, under Chinese law, be eligible for the death penalty."

Shaikh's family and campaigners say he showed signs of mental illness before he moved to Poland several years ago and his mental condition, most likely bipolar disorder, deteriorated. He had been duped into carrying drugs by a gang who exploited his delusions that he was going to China to be a pop star, they say.

Reprieve has located a recording of a song Shaikh wrote in English, Polish and Arabic and says it helps illustrate his long history of strange behaviour.

Urumqi is capital of the far western region of Xinjiang, where 22 people have so far been sentenced to death – with at least nine executions already carried out – over ethnic rioting earlier this year.

A Foreign Office spokeswoman said: "We have made representations at the highest possible levels. The prime minister wrote to the Chinese government on 21 December and the foreign secretary has also written. We have made our position to the Chinese authorities quite clear. The prime minister, ministers and other officials have been and remain closely engaged."

A spokesman for the British embassy in Beijing said: "We deeply regret that mental health concerns had no bearing on the final judgment despite requests by Mr Shaikh's lawyers and repeated calls by the prime minister, ministers, members of the opposition as well as the European Union.

"This is obviously distressing for the family. Our thoughts are with them at this difficult time. We continue to provide them with support."